Szegö kernel asymptotics and Morse inequalities on CR manifolds

Abstract

ABSTRACT. Let be an abstract compact orientable CR manifold of dimension ¾Ò ½, Ò ¾, and let Ä be the -th tensor power of a CR complex line bundle Ä over . We assume that condition ´Õµ holds at each point of . In this paper we obtain a scaling upper-bound for the Szegö kernel on´¼ Õµ-forms with values in Ä , for large . After integration, this gives weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities. We apply the strong Morse inequalities to the embedding of some convexconcave manifolds.

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